1

Abstract

This work details a preliminary design for a gravity dam to be built with roller

compacted concrete (RCC), located in central Portugal. Some design aspects are

emphasized, related to the adoption of a tentative section with gallery satisfying

geometric and construction constraints, as well as aspects associated with safety of

the structure and adjoining foundation. Although a preliminary analysis for the

initial geometry proved structurally safe, a plane stress finite element analysis

indicated the need for geometric refining insuring safety under a specific seismic

load combination. An improved section for the dam was achieved, inducing safe

detailed patterns of stresses and displacements for the dam and foundation.

Keywords: dams, roller compacted concrete, finite elements, optimised shape,

preliminary design, Ribeiradio RCC dam.

1 Introduction

The mankind constant need of water for its survival motivated, throughout the ages,

the construction of dams. In particular, the one referred in this work will be located

in river Vouga in central Portugal, near Ribeiradio village and 8 km upstream of the

town of Sever do Vouga.

With a storage capacity beyond 108 m3, it will constitute a source for public water

supply and industrial water supply for both population/industrial demands of

townships along Vouga hydrological basin, as well as for agriculture usage in the

fertile Vouga valley. Additionally, it will also be quite useful in river flood control

of the lower part of the river Vouga, dampening the effects of characteristic flood

rates and reducing flood frequency and severity, namely in the vicinity of the city of

Águeda. The hydraulic structure will still provide a hydroelectric power of 10 MW,

also important for the paper-pulp industries of the zone.

2

As outlined by Hansen and Reinhardt [1] roller-compacted concrete (RCC) has

become one of the most widely used materials for modification and upgrading of

aging embankment dams in the USA, with inherent dam safety and appearance.

Moreover, the RCC techniques made also possible to use RCC gravity dams as an

economically competitive alternative to conventional concrete or embankment dams.

The possibility of rapid construction at low cost constitutes the major advantage of

RCC dams. Because of their horizontal method of construction, stepped spillways

and outlet works are incorporated as an integral part of the RCC structure, with a

reduced velocity at the toe of the spillway. Also because of shorter construction

periods, the river diversion and the potential need of cofferdams are significantly

minimised, especially for large rivers.

Based on these advantages and also on the facts that the crest elevation and

footprint for a RCC dam are considerably and invariably less than for embankment

dams, it is not surprising that the Portuguese authorities planned a RCC dam for

such a convenient site. Moreover the specification of continuous placement of RCC,

minimising cold joints between horizontal layers, would allow contractors bids at

lower unit prices for a dam construction with little risk.

Tendering and the subsequent bidding are increasingly becoming an essential

component of procurement in a wide range of industrial private and public sectors,

including the service industry of engineering consultancy and construction. As

owner of the future hydraulic structure, Portuguese Water Resources and

Environment Ministry (INAG ‘Instituto da Água’) promoted in June 2000 an

international tendering, involving simultaneously conception and construction of the

RCC dam, in order to select the most technically qualified construction consortium.

The 6 distinct construction partnerships that answered to the call until December

2000, organized their candidacies, proposed alternative technical solutions and

submitted their construction bids, based on a provided reference solution of a

preliminary study conducted earlier by COBA in 1999 [2]. This permitted INAG to

classify and rank partnerships through more open, transparent, fair, more

coordinated, efficient and more cost-effective selection practices.

2 Improved Alternative Solution for Ribeiradio Dam

The preliminary design calculations and subsequent finite element analysis, partially

shown in the present paper, resulted from consultancy services permitting the

attendance of a participating partner in the international public tendering promoted

by INAG in 2000, associated with the construction of the above-mentioned RCC

dam. It is typical of similar analysis done at standard civil engineering consultancy

offices throughout Portugal, as a clear indication of continuous technical updating

and upgrading in the art of engineering design.

In order to permit a fair biding of the construction costs of the required complete

dam infrastructure, an alternative more economic solution was searched, whose

structural strength integrity and safety had to be assessed. The alternative solution

proposed was based on minimising the construction costs per unit length, on the

basis of the following sketch of fixed and variable parameters of an idealized

simplified cross section of the gravity dam (Figure 1).

3

The restrictions established on these geometric parameters where either

operational or on the basis of the reference solution [2]. Such set of optimised

dimensions (minimising costs and therefore cross section areas) permitted a

preliminary efficient evaluation of dam safety as a beam under composite flexure

and of its stability as a rigid body. Only under these circumstances would a further

finite element analysis be performed for the evaluation of the generalized stresses

and displacements in the dam core, interface and foundation medium.

y

3b

O

Rd

h3

h 1

Pr(xr,yr )

)yc,c x( cP

O1 B x1b2O

2h

Figure 1: Sketch of the cross section geometry for optimisation

Assume B=51.75 m, H=64.25 m, b3=7.75 m and h3= 10.75 m to be fixed

quantities as given by the reference solution [2]; also assume b1, h1 and R to be

variable quantities subjected to the restrictions

H 0.6 h H 0.4

5

1

11

lim

21

tghb

mdPPd

hhH

cr

such that Rbx 30 and 30 hy .

Minimising the area 222

1

222211

211

2 ABHhbR

BHhbRBHA

is equivalent to maximising the area increment l1

22

1

2 hbRtghRA .

But more precisely it is equivalent to maximising the difference in costs per unit

length, associated with the substitution of RCC from the dam core by RCC and

structural concrete at the bottom apron of the upstream face. Such cost difference is

safely expressed by 11

2

cos hbCRCA SCRCCt , where RCCC is the local unit cost

of an m3 of RCC and SCC is the local unit cost of a m3 of structural concrete.

4

Conceptually the potential economic gains would be associated with the creation

of a large cavity or gallery at the dam core and its substitution by an inclined bottom

area also of RCC but with a surface finishing in structural concrete to be

continuously submerged. The construction, economic and technical advantages of

using RCC would still be fully exploited, with a very small increase of the costs of

the upstream structural concrete plus the costs of slip form or precast concrete

gallery units or of conventional forming method. Further geometric deductions

detailed by Barros [3] permitted to obtain the following Table 1 of possible radius

for the geometric implantation of the semi-circular gallery at the dam core.

d (m) 10 11 12 13 14 15 16 17 18 19 20

R (m) 9.85 9.3 8.7 8.2 7.6 7 6.5 5.9 5.35 4.8 4.2

Table 1: Limiting radius imim dR for the geometric implantation of the gallery

Local construction indexes relate approximately RCC and structural concrete

costs by SCRCC C%60C , so that the function to be maximised is now

gg sRsRF 0156.10326.0),( 2 . From this it follows that the limit cavity radius

corresponding to null gain (or null economic added value) would be gsR 5.547

where gs is the slope gradient of the upstream bottom face. For an initial choice of

%10gs , permitting to minimise corners and concrete formworks at the bottom

upstream face near the water intake, it follows that mR 39.710.05.547limit

beyond which effective economic gains occur. Using mR 5.7 as initial value of

the arc radius, then md 14 and mb 35.31

.

Evaluation of dam safety as a beam under composite flexure, calculated the

compressive stresses at the downstream and upstream feet of the dam core as 1.0 and

0.4 MPa respectively. Since sufficient slack appears to exist for the compressive

stress values at dam feet, further economic gains where attempted by extending

vertically (about 12 m) the cavity to the foundation, therefore assuming an arc-

rectangle shape. The safety of the proposed RCC dam with this new arc-rectangle

gallery was then ascertained with respect to its strength, stiffness and base stability,

under several combinations of load cases.

The preliminary strength study performed by Barros [3] is synthesized in Table 2,

where safe values for the normal stresses (+, compressive) at the upstream and

downstream dam feet MPa/m,and du are given for different load cases. These

load cases are combinations of self-weight W, hydrostatic pressure Ph without and

with bottom-uplift U, and horizontal earthquake E acting on the empty and full

reservoir in two possible senses (upstream to downstream du , and inversely).

The seismic actions are modelled by equivalent static forces on the basis of the

maximum local seismic acceleration seismica 0.1g m/s2 (with return period of 1000

years), proposed by Oliveira [4] in the standard characterization of seismic hazards

and evaluation of the seismic risk in Portugal.

5

Load Case u d

W 1.20 0.12

W+Ph 0.74 0.66

W+Ph+U 0.10 0.66

Empty reservoir

W+Eud

W+Edu

W+Edu (RCC without tractions)

1.04

1.36

1.57

0.28

-0.04

0.00

Full reservoir

W+Ph+U+ Edu

W+Ph+U+ Eud

W+Ph+U+ Eud (RCC without tractions)

0.34

-0.14

0.00

0.42

0.90

1.11

Table 2: Load cases for strength study

The stiffness study is performed calculating the dam crest total lateral

displacement and comparing it with admissible values. The lateral displacement

contributions, estimated according to the practical methodologies proposed by

Herzog [5], take into account flexure and shear deformations of the concrete

)45.4( mmwconc , flexure and shear deformations of the foundation

)68.5( mmw found , upstream rotation of the valley bottom )25.2( mmwrot and

thermal gradient between upstream and downstream faces )84.1/( mmwtemp

measured conveniently 1 m below the surface and inside the dam core concrete

mass. The total estimated dam crest lateral displacement varies between a minimum

of –1.84 mm -2 mm upstream (when the reservoir is empty and the downstream

face is the warmest) and a maximum of 4.45+5.68-2.25+1.84=9.7 mm 1 cm

downstream (when the reservoir is full and the downstream face is the coolest).

The base stability of the dam (with arc-rectangle gallery) against sliding as a rigid

block was evaluated without and with earthquake occurrence, assuming the

indentation of the dam core on the foundation base as suggested in the reference

solution. The safety factors obtained were respectively 1.5 and 1.2, using very small

stress values of 0.1 MPa for the adherence between the concrete and the foundation.

3 Global Stability Analysis

The design and constructed quality of lift surfaces are critical to the stability and

seepage performance of the RCC dam. Since RCC is often placed in 250-400 mm

thickness layers and subsequently compacted, the global stability of the RCC dam is

an essential issue to verify at each dam elevation associated with successive lifts.

The need to minimise the number of cold joints, between horizontal layers of

successive lifts, is also indicative of the number of verifications of RCC dam global

stability at each elevation, calculating the sliding safety factor according to the

following relation between the active and reactive forces:

6

forcesActive

forcesReactiveSLIDINGF

(1)

The active forces result from the water pressure acting on the upstream face of

the dam, while the reactive forces are guaranteed by the horizontal frictional forces

RDFH mobilized in the surface between concrete layers of RCC or between concrete

and the foundation soil. The latter are expressed by:

ActgFH ddnRD ' (2)

where n are the local normal stresses at each element area A , dc is the design

cohesion and '

d is the design friction angle. The design values of the geotechnical

parameters (cohesion and friction angle) were obtained from the prescriptions of

Eurocode 7 [6], dividing the characteristic values kc and '

k by the corresponding

partial safety factors, respectively c and , as expressed in equations (3) and (4).

'' kd

tgarctg

c

k

d

cc

(3)

(4)

The partial safety factors and c are shown in the following Table 3, for the two

types of analyses to be performed.

Analysis ’ c

Static 1.5 4.0

Dynamic 1.1 3.0

Table 3: Geotechnical partial safety factors

The characteristic values of the geotechnical parameters for global stability

analysis are given in Table 4, for the two types of interface zones between

contacting materials.

Surface '

k (degrees) kc (kPa)

Concrete-concrete (RCC) 42.0 550.0

Concrete-foundation 45.0 400.0

Table 4: Characteristic values of geotechnical parameters

The potential sliding stability at the elevations of the cold joints proposed in the

reference solution [2] was ascertained, and the corresponding sliding safety factors

are synthesized in the following Table 5 extracted from [7].

7

Height of Sliding Surface (m) Sliding Safety Factor

40 1.35

50 1.49

60 1.60

70 1.81

80 2.08

Table 5: Sliding safety factors for different heights

4 Finite Element Analysis

Since the previous preliminary analyses have been successfully performed for the

original and improved optimised cross section, ascertaining the overall or global safe

performance and behaviour of the RCC dam, a detailed local analysis by the finite

element method seems now quite justifiable. Such analysis will characterize the

pattern of generalized stresses and displacements of the complete model, namely in

the RCC core, at the interface between dam and foundation, and in all the modelled

portion of the foundation soil.

4.1 Finite Element Model

The structural behaviour of the dam’s critical cross section (Figure 2) was modelled

with an eight-node parabolic finite element mesh, in order to simulate the plain

stress state installed in the concrete of the RCC dam and in the material of the

foundation underneath.

Figure 2: Dam critical cross section

Since on one hand this was a preliminary study and on the other hand a cost

minimisation (optimisation of the weight lightening gallery with respect to

dimensions and location), a coarse mesh was used to obtain a first approximation of

the stress level and the magnitude of expected displacements for each tested

geometry.

8

The two meshes tested during finite element modelling are visualised in Figure 3,

obtained through the use of VIFEM software (Visual Interface for Finite Element

Method) developed by Teixeira [8]. The original geometry refers to the arc-rectangle

gallery proposed for preliminary analysis; the improved geometry corresponds to a

decrease of its dimensions with a more downstream implantation in the dam core.

Original geometry Improved geometry

Figure 3: Finite element meshes

The structural behaviour of the dam could only be modelled with acceptable

accuracy taking in account the existing interaction between the RCC core and the

foundation material on which the dam rests. According to Figure 4 a certain amount

of surrounding soil was also meshed, with the purpose of minimising the boundary

effects due to the finite character of the mesh.

Figure 4: Finite element mesh of dam and foundation, for the improved geometry

9

The boundary conditions considered correspond to a rigid link to the bottom layer

of the foundation material and horizontal restriction to movement on both vertical

boundaries of the meshed domain.

The mechanical properties of the materials involved in the simulation of both the

foundation and the RCC core of the dam are shown in the following Table 6, where

E is the elastic modulus, the Poisson ratio and the specific volumetric weight.

Material E (GPa) (kN/m3 )

1 - Foundation 2 0.35 19

2 - RCC 20 0.22 24

Table 6: Material data for the design of the RCC dam

4.2 External Loads

The external loads applied to the RCC dam for this finite element analysis are the

sum of two kinds of forces. The first kind corresponds to mass forces mxf and myf

due to seismic and gravity accelerations, respectively in the x and y directions,

calculated per unit volume by:

3/45.2 mkNg

af concrete

seismic

mx (5)

3/24 mkNf concretemy (6)

The term seismica is the maximum horizontal ground acceleration (here acting in

the body of the dam), which was already justified to assume the value of 1.0 m/s2.

The second kind of forces represents the external pressures induced by the water

on the upstream face of the dam (Figure 5), including the hydrodynamic term

accounting for the seismic effect in the water mass, calculated with Westergard’s

parabola [9]. The hydrostatic and hydrodynamic pressures are given respectively by

yHyp waterchydrostati )( (7)

2

2

1)(H

yKypseismic (8)

Figure 5: Hydrostatic and hydrodynamic pressures on the upstream face

10

where mH 75 is the maximum height of water in the reservoir, water is the water

volumetric specific weight and the scaling factor Hg

aK water

seismic .

4.3 Stresses and Displacements

In the next figures are shown the results of the stress and displacement finite element

calculations associated with the seismic load case, in terms of principal stresses

(1,2,3) and total displacements of the deformed mesh, also obtained using VIFEM software [8]. Figures 6 to 9 refer to the preliminary original geometry of the

arc-rectangle gallery at the RCC dam core.

Preliminary original geometry

Stresses 1

Stresses 3

Stresses 2 Deformed mesh

With the purpose of reducing the stress levels around the gallery and near the

upstream bottom apron, the same calculations were performed for the suggested

improved geometry and implantation of the arc-rectangle gallery at the RCC dam

core, nevertheless satisfying the mentioned geometric and operational restrictions.

11

The following Figures 10 to 13 refer to such improved geometry, associated with

a decrease of the gallery dimensions and a more downstream implantation in the

RCC dam core, and illustrate substantial reductions in the values of the generalized

quantities represented in the two distinct solutions.

Improved geometry and implantation

Stresses 1

Stresses 3

Stresses 2 Deformed mesh

4.4 Safety Analysis

With the knowledge of the distribution and values assumed by the principal stresses

for the seismic load case, a verification of the safety of the dam has to be carried out

at critical points based on a reasonable yielding criterion. Barros [10,11] used earlier

a similar approach and methodology, when comparing less refined and established

yielding criteria for concrete in dams under biaxial state of stress, nevertheless

appropriate and conservative for preliminary design.

Herein the one proposed in the CEB-FIP Model Code 1990 [12] for biaxial stress

state of concrete will be used, with the necessary characteristics of the RCC.

Designate by 31 the ratio of minimum to maximum principal stresses.

12

At failure (f) under biaxial state-of-stress the yielding criterion of concrete,

represented in Figure 14, is expressed by

fck)ompression(Biaxial C f 23)1(

80.31

(9)

fctkfck

n)Compressio(Traction f

3

1 80.01

(10)

fctkTraction)(Biaxial f 1 (11)

where the characteristic values used herein for the compressive strength of RCC

(after a cure of 90 days) and for the tensile strength of RCC are respectively

MPafck 1290 and MPafctk 1.1 .

-1.30

-1.10

-0.90

-0.70

-0.50

-0.30

-0.10

0.10

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

1f,2f,3f (x fck)

1

f,

2f,

3f (x

fck)

Eq. 3.2a

Eq. 3.2b

Eq. 3.3a

Eq. 3.3b

Eq. 3.4

Figure 14: Yielding of concrete under biaxial state-of-stress

Figure 15 illustrates quite efficiently the comparison between the results of the

yielding zones associated with the seismic load case, obtained here for the

preliminary initial geometry tested (larger gallery) and for the improved geometry

and implantation (smaller gallery towards downstream). It is evident from the

relative comparison that the yielding stripe or traction band developing at 45º (for

the initial geometry) between the upstream bottom toe and the gallery upstream side,

is reduced to an incipient formation of a yielding zone due to stress concentration

and almost disappearing thereafter (for the improved geometry).

13

Initial geometry Improved geometry Figure 15: Yielding zones for the two different geometries

It should be emphasized that the potential yielding zones for the RCC dam are

located at places where conventional structural concrete is adequately used, with

strength characteristics far superior to the ones for RCC being used in the yield

criterion. Therefore, the previous analyses are conservative estimates. Moreover,

other adjustments on the gallery size and location can be efficiently accomplished

satisfying other required restrictions.

In view of the fact that structural safety of the RCC is as important as the

geotechnical safety of the foundation, an assessment was made of the stress patterns

and magnitudes at various foundation levels. For the two foundation levels

represented in Figures 16 and 17, the stress assessment along the surface (1-1’)

corresponds to the interface with the dam, while the other stress assessment occurs

in a deeper foundation layer (2-2’) around 15 meters below the reservoir bottom.

Figure 16: Distribution of vertical stresses in the dam-foundation finite block

14

Figure 17: Vertical stresses (y) on foundation, along two surfaces

In Figure 17, the trends and magnitudes of the vertical stresses along line 1-1’

reveal the expectable influence of boundaries and discontinuities. However the

trends and magnitudes of the vertical stresses along line 2-2’ are much more realistic

in terms of being able to describe the true vertical stress evolution across the

foundation at this depth. The peek value of 1.4 MPa is quite safe in terms of the

expected compressive strength values of the bed-layer at the site (around 10 MPa).

4 Conclusion A preliminary design for a gravity dam to be built with roller compacted concrete,

located in central Portugal, was thoroughly detailed. The international tendering and

bidding for conception and construction was justified. Design aspects were

emphasized related to the adoption of a gallery satisfying geometric and construction

constraints, as well as aspects associated with safety of the structure and adjoining

foundation. A preliminary analysis for the initial geometry proved structurally safe,

under strength stiffness and stability criteria. A plane stress finite element analysis

calculated accurate values of generalized stresses and displacements of the dam and

foundation. A safety analysis of the biaxial state-of-stress was performed according

to the CEB-FIP Model Code 1990, indicating the need for geometric refining

insuring safety under a specific seismic load combination. The improved section for

the dam with a smaller gallery positioned more downstream at the dam core,

induced safe detailed patterns of stresses and displacements for the dam and

foundation. The comparison of the yielding zones of the two studied geometries is

an important tool to ascertain the safety of distinct dam solutions.

15

References

[1] K.D. Hansen and W.G. Reinhardt, “Roller Compacted Concrete Dams”,

McGraw-Hill Book Company Inc., New York, 1991.

[2] COBA, “Aproveitamento de Ribeiradio”, Solução de Referência realizada

para o Instituto da Água (INAG), COBA-Consultores de Engenharia e

Ambiente, Lisboa, 1999.

[3] R.C. Barros, “Solução Estrutural Alternativa para a Barragem de Ribeiradio

(Geometria Optimizada com Galeria Arco-Rectângulo)”, Relatório Técnico

Interno BAH-1/00, Engedec, Porto, 2000.

[4] C.S. Oliveira, “O Risco Sísmico em Portugal e sua Influência na Segurança

Estrutural das Construções”, L.N.E.C., Serviço de Estruturas - Divisão de

Dinâmica Aplicada, Proc. 36/11/4394, Lisboa, 1979.

[5] M.A.M. Herzog, “Practical Dam Analysis”, Thomas Telford Publishing

Limited, London, UK, 1999.

[6] Eurocode 7, “Geotechnical Design – Part 1: General Rules”, prEN 1997-1,

CEN-European Committee for Standardisation, Brussels, 2001.

[7] FL-engenharia, “Barragem de Ribeiradio: Dimensionamento e

Características da Barragem e da Fundação”, Relatório de Consórcio

Concepção-Construção, Porto, 2000.

[8] R.T. Teixeira, “Análise de Problemas de Grandes Deformações em

Geotecnia”, M.Sc. thesis in Structural Engineering, Dept of Civil

Engineering, FEUP, Porto, Portugal, 2001.

[9] N.M. Newmark and E. Rosenblueth, “Fundamentals of Earthquake

Engineering”, Prentice Hall, Inc., Englewood Cliffs, N.J., 1971.

[10] R.C. Barros, “A Avaliação de Estados Biaxiais de Tensão no Betão”, in

“Proceedings of the Confª Ibero-Americana sobre Aproveitamentos

Hidráulicos”; Vol.1, Tema A: Projecto, pp. 271-278; Vol. 3, Tema A:

Projecto de Barragens de Betão - Dimensionamento (Critérios e Modelos),

pp. 121-122, 133 and 142; LNEC, Lisboa, Portugal, 1987.

[11] R.C. Barros, “A Avaliação de Estados Biaxiais de Tensão no Betão”,

Concreto nº 161, pp. 35-39, Ed.: Associação dos Industriais de Construção

Civil e Obras Públicas do Norte (AICCOPN), Porto, 1999.

[12] CEB, “CEB-FIP Model Code 1990: Design Code”, Comité Euro-

International du Béton, Lausanne 1991 & 1993, Thomas Telford Services

Ltd., London, 1993.